Math / Algebra

QuestionGabriella and Ming are selling cookie dough for a school fundraiser. Customers can buy packages of white chocoloate chip cookie dough and packages of gingerbread cookie dough. Gabriella sold 11 packages of white chocoloate chip cookie dough and 2 packages of gingerbread cookie dough for a total of $\$ 225$ . Ming sold 8 packages of white chocoloate chip cookie dough and 10 packages of gingerbread cookie dough for a total of $\$ 326$ . What is the cost each of one package of white chocoloate chip cookie dough and one package of gingerbread cookie dough?

Studdy Solution

STEP 1

1. Gabriella sold 11 packages of white chocolate chip cookie dough and 2 packages of gingerbread cookie dough for a total of \$225.
2. Ming sold 8 packages of white chocolate chip cookie dough and 10 packages of gingerbread cookie dough for a total of \$326.
3. We need to find the cost of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough.

STEP 2

1. Define variables for the unknowns.
2. Set up a system of equations based on the given information.
3. Solve the system of equations using an appropriate method (substitution or elimination).
4. Interpret the solution to find the cost of each type of cookie dough.

STEP 3

Define variables for the unknowns.
Let $x$ be the cost of one package of white chocolate chip cookie dough, and $y$ be the cost of one package of gingerbread cookie dough.

STEP 4

Set up a system of equations based on the given information.
From Gabriella's sales, we have: $11x + 2y = 225$
From Ming's sales, we have: $8x + 10y = 326$

STEP 5

Solve the system of equations using the elimination method.
First, we will multiply the first equation by 5 to align the coefficients of $y$ :
$5(11x + 2y) = 5 \times 225$ $55x + 10y = 1125$
Now, subtract the second equation from this new equation to eliminate $y$ :
$(55x + 10y) - (8x + 10y) = 1125 - 326$ $47x = 799$
Solve for $x$ :
$x = \frac{799}{47}$ $x = 17$

STEP 6

Now that we have $x = 17$ , substitute this value back into one of the original equations to solve for $y$ . We'll use the first equation:
$11(17) + 2y = 225$ $187 + 2y = 225$
Subtract 187 from both sides:
$2y = 225 - 187$ $2y = 38$
Divide by 2:
$y = \frac{38}{2}$ $y = 19$

STEP 7

Interpret the solution.
The cost of one package of white chocolate chip cookie dough is $\$17$ , and the cost of one package of gingerbread cookie dough is $\$19$ .

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the unknowns.
2. Set up a system of equations based on the given information.
3. Solve the system of equations using an appropriate method (substitution or elimination).
4. Interpret the solution to find the cost of each type of cookie dough.

STEP 3

Define variables for the unknowns.
Let $x$ be the cost of one package of white chocolate chip cookie dough, and $y$ be the cost of one package of gingerbread cookie dough.

STEP 4

Set up a system of equations based on the given information.
From Gabriella's sales, we have: $11x + 2y = 225$
From Ming's sales, we have: $8x + 10y = 326$

STEP 5

STEP 6

Now that we have $x = 17$ , substitute this value back into one of the original equations to solve for $y$ . We'll use the first equation:
$11(17) + 2y = 225$ $187 + 2y = 225$
Subtract 187 from both sides:
$2y = 225 - 187$ $2y = 38$
Divide by 2:
$y = \frac{38}{2}$ $y = 19$

STEP 7

Interpret the solution.
The cost of one package of white chocolate chip cookie dough is $\$17$ , and the cost of one package of gingerbread cookie dough is $\$19$ .

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the unknowns.2. Set up a system of equations based on the given information.3. Solve the system of equations using an appropriate method (substitution or elimination).4. Interpret the solution to find the cost of each type of cookie dough.

STEP 3

Define variables for the unknowns.Let x x x be the cost of one package of white chocolate chip cookie dough, and y y y be the cost of one package of gingerbread cookie dough.

STEP 4

Set up a system of equations based on the given information.From Gabriella's sales, we have: 11x+2y=225 11x + 2y = 225 11x+2y=225From Ming's sales, we have: 8x+10y=326 8x + 10y = 326 8x+10y=326

STEP 5

STEP 6

STEP 7

Interpret the solution.The cost of one package of white chocolate chip cookie dough is $17 \$17 $17, and the cost of one package of gingerbread cookie dough is $19 \$19 $19.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define variables for the unknowns.
2. Set up a system of equations based on the given information.
3. Solve the system of equations using an appropriate method (substitution or elimination).
4. Interpret the solution to find the cost of each type of cookie dough.

Define variables for the unknowns.
Let $x$ be the cost of one package of white chocolate chip cookie dough, and $y$ be the cost of one package of gingerbread cookie dough.

Set up a system of equations based on the given information.
From Gabriella's sales, we have: $11x + 2y = 225$
From Ming's sales, we have: $8x + 10y = 326$

Interpret the solution.
The cost of one package of white chocolate chip cookie dough is $\$17$ , and the cost of one package of gingerbread cookie dough is $\$19$ .